A001314 Number of (unordered) ways of making change for n cents using coins of 2, 5 (two kinds), 10, 20, 50 cents.

1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 5, 2, 5, 2, 5, 8, 5, 8, 5, 8, 15, 8, 15, 8, 15, 22, 15, 22, 15, 22, 35, 22, 35, 22, 35, 48, 35, 48, 35, 48, 70, 48, 70, 48, 70, 92, 70, 92, 70, 92, 127, 92, 127, 92, 127, 162, 127, 162, 127, 162, 215, 162, 215, 162, 215, 268

Offset

0,6

References

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.

G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 183

Index entries for sequences related to making change.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 1, 0, -1).

Maple

1/(1-x^2)/(1-x^5)^2/(1-x^10)/(1-x^20)/(1-x^50)

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^5)^2 (1 - x^10) (1 - x^20) (1 - x^50)), {x, 0, 50}], x]
Table[Length[FrobeniusSolve[{2, 5, 5, 10, 20, 50}, n]], {n, 0, 70}] (* Harvey P. Dale, Sep 23 2023 *)

Crossrefs

Sequence in context: A166478 A050325 A332510 * A020733 A210700 A215745

Adjacent sequences: A001311 A001312 A001313 * A001315 A001316 A001317

Keyword

nonn

Author

N. J. A. Sloane

Status

approved